Penny Fab Model

Chapter 6: A Science of ManufacturingChapter 7: Basic Factory Dynamics

ENGM 663 Paula Jensen

Agenda

•Factory Physics • Chapter 6: A Science of Manufacturing (From 2nd Ed)• Chapter 7: Basic Factory Dynamics• (New Assignment Chapter 6: Problem 1• Chapter 7: Problems 5, 8, 10)•Test 1 Study Guide

Objectives, Measures, and Controls

I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but have scarcely, in your thoughts, advanced to the stage of Science, whatever the matter may be.

– Lord Kelvin

Why a Science of Manufacturing?

• Confusion in Industry:• too many “revolutions”• management by buzzword• sales glitz over substance

• Confusion in Academia:• high-powered methodology applied to non-problems• huge variation in what is taught

• Example of Other Fields:• Civil Engineering–statics, dynamics• Electrical Engineering – electricity and magnetism• Many others

Automobile Design• Requirements:

• Mass of car of 1000 kg• Acceleration of 2.7 meters per second squared (zero to 60 in 10

seconds)• Engine with no more than 200 Newtons of force

• Can we do it?

• Answer: No way!

F = ma

200 Nt (1000 kg) (2.7 m/s2) = 2,700 Nt.

Factory Design• Requirements:

• 3000 units per day,• with a lead time of not greater than 10 days,• and with a service level (percent of jobs that finish on time) of at

least 90%.

• Can we do it?

• Answer:

?Who knows?

Factory Tradeoff Curves

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

74 77 81 85 89 93 97

Service in %

Le

ad

Tim

e(d

ays

)

2400 2600 2800 3000

Goals of a Science of Manufacturing• Tools:

• descriptive models • prescriptive models• solution techniques

• Terminology:• rationalize buzzwords• recognize commonalities across environments

• Perspective:• basics• intuition• synthesis

The Nature of Science• Purpose:

The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypothesis or axioms.

--- Albert Einstein• Steps:

1. Observation.2. Classification.3. Theoretical Conjecture.4. Experimental verification/refutation.5. Repeat.

Systems Analysis• Definition: Systems analysis is a structured approach to problem-solving

that involves

1. Identification of objectives (what you want to accomplish), measures (for comparing alternatives), and controls (what you can change).

2. Generation of specific alternatives.3. Modeling (some form of abstraction from reality to facilitate

comparison of alternatives).4. Optimization (at least to the extent of ranking alternatives and

choosing “best” one).5. Iteration (going back through the process as new facets arise).

System Analysis Paradigm

Evaluate System PerformanceLook For Oversights

Identify Future Opportunities

Implement PoliciesTrain Users

Fine Tune System

Conjecture ObjectivesVerify constraints

Identify Alternatives

Compare AlternativesChoose Policies

Ask “What If” Questions

REAL WORLD

Choose Measures of EffectivenessSpecify Parameters and Controls

Model InteractionsVerify & Validate Model

Compare ControlsOptimize Control Levels

Sensitivity Analysis

Validate Model PredictionsQuestion AssumptionsIdentify Other Controls

ANALOG WORLDOPERATIONSANALYSIS

SYSTEMSDESIGN

IMPLEMENTATION

EVALUATION

General Measures and Objectives

• Fundamental Objective:• elementary starting point• source of agreement• example - make money over the long-term

• Hierarchy of Objectives:• more basic objectives that support fundamental objective• closer to improvement policies

• Tradeoffs:objectives conflict• we need models

Hierarchical ObjectivesHigh

Profitability

LowCosts

Low UnitCosts

High Throughput

Less Variability

High Utilization

LowInventory

QualityProduct

HighSales

Many products

Fast Response

MoreVariability

High Inventory

LowUtilization

ShortCycle Times

High CustomerService

Corporate Measures and Objectives• Fundamental Objective: Maximize the wealth and well-being of the

stakeholders over the long term.

• Financial Performance Measures: 1. Net-profit.2. Return on investment.

• Components: 1. Revenue.2. Expenses.3. Assets.

Plant Measures and Objectives• Measures:

• Throughput: product that is high quality and is sold.• Costs: Operating budget of plant.• Assets: Capital equipment and WIP.

• Objectives:• Maximize profit.• Minimize unit costs.

• Tradeoffs: we would like (but can’t always have)• Throughput• Cost• Assets

Systems Analysis Tools• Process Mapping:

• identify main sequence of activities• highlight bottlenecks• clarify critical connections across business systems

• Workshops:• structured interaction between various parties• many methods: Nominal Group Technique, Delphi, etc.• roles of moderator and provocateur are critical

Systems Analysis Tools (cont.)• Conjecture and Refutation:

• promotes group ownership of ideas• places critical thinking in a constructive mode• everyday use of the scientific method

• Modeling:• always done with specific purpose• value of model is its usefulness• modeling is an iterative process

The Need for Process Mapping• Example: North American Switch Manufacturer -- 10-12 week leadtimes

in spite of dramatically reduced factory cycle times:

10% Sales15% Order Entry15% Order Coding20% Engineering10% Order Coding15% Scheduling5% Premanufacturing and Manufacturing10% Delivery and Prep

• Conclusion: Lead time reduction must address entire value delivery system.

Process Mapping Activities• Purpose: understand current system by

• identifying main sequence of activities• highlighting bottlenecks• clarifying critical connections across business system

• Types of Maps:• Assembly Flowchart: diagram of activities to assembly product.• Process Flowchart: diagram of how pieces of system interrelate

in an organization.• Relationship Map: diagram of specific steps to accomplish a task,

without indication of functions or subsystems.• Cross-Functional Process Map: diagram of specific steps to

accomplish a task organized by function or subsystem responsible for the step.

Sample Assembly FlowchartCELL 1

START

PANASERT1050

ROBOT1100

CIM FLEX1250

ROBOT1150

ROBOT1200

ROBOT1300

ROBOT1350

ROBOT1375

SOLDER STATION1000

LASER TRIM1775

DECODERSINGULATION

ROBOT1500

RECEIVERSINGULATION

ROBOT1750EOL TEST

1550

CELL 2

UNIX CELL CONTROLLER TEST BAYLEGEND

ROBOT1380

Process Flowchart for Order Entry

CustomerApproval?

Approval?

End ofBucket?

Review Plan/Lists

Enter Parts Listsinto System

Generate PartsLists

Yes

Generate StandardLayout Plan

Receive CustomerOrder Form

Generate CuttingOrders

No

Yes

Yes

No

No

Sample Relationship Map

Order Processing

ProductionScheduling

Design Fabricating Finishing Shipping

WarehouseCustomers

Salesmen Production control

Salesmancontrols the

order processingand design flow

ProductionControl -

controls workflow

Operatingdepartments make

independentdecision

Sample Cross-Functional Process Map

Customer needsobserved

Marketopportunity

defined

New product

evaluated

New productconceptfloated

Process feasibilityreview and

cost estimating

New productprototypedeveloped

Field supportneeds reviewed

Price anddistribution

options reviewed

Field supportplanned

Tooling andcapacityplanned

Productionreadinessplanned

Final productengineered

Pricepoint set

Production

FieldOffices

Marketing

Engineering

Manufacturing

TIME

Roll-outplanned

Conclusions• Science of Manufacturing:

• important for practice• provides a structure for OM education

• Systems Approach:• one of the most powerful engineering tools• a key management skill as well (e.g., re-engineering)

• Modeling:• part, but not all, of systems analysis• key to a science of manufacturing• more descriptive models are needed

Basic Factory Dynamics

Physics should be explained as simply as possible, but no simpler.

– Albert Einstein

HAL Case• Large Panel Line: produces unpopulated printed circuit boards

• Line runs 24 hr/day (but 19.5 hrs of productive time)

• Recent Performance:• throughput = 1,400 panels per day (71.8 panels/hr)• WIP = 47,600 panels• CT = 34 days (663 hr at 19.5 hr/day)• customer service = 75% on-time delivery

What data do we need to decide?

Is HAL lean?

HAL - Large Panel Line Processes

• Lamination (Cores): press copper and prepreg into core blanks• Machining: trim cores to size• Internal Circuitize: etch circuitry into copper of cores• Optical Test and Repair (Internal): scan panels optically for defects• Lamination (Composites): press cores into multiple layer boards• External Circuitize: etch circuitry into copper on outside of composites• Optical Test and Repair (External): scan composites optically for defects• Drilling: holes to provide connections between layers• Copper Plate: deposits copper in holes to establish connections• Procoat: apply plastic coating to protect boards• Sizing: cut panels into boards• End of Line Test: final electrical test

HAL Case - Science?• External Benchmarking

• but other plants may not be comparable

• Internal Benchmarking• capacity data: what is utilization?• but this ignores WIP effects

Need relationships between WIP, TH, CT, service!

Definitions

• Workstations: a collection of one or more identical machines.• Parts: a component, sub-assembly, or an assembly that moves

through the workstations.• End Items: parts sold directly to customers; relationship to

constituent parts defined in bill of material.• Consumables: bits, chemicals, gasses, etc., used in process but do

not become part of the product that is sold.• Routing: sequence of workstations needed to make a part.• Order: request from customer.• Job: transfer quantity on the line.

Definitions (cont.)

• Throughput (TH): for a line, throughput is the average quantity of good (non-defective) parts produced per unit time.

• Work in Process (WIP): inventory between the start and endpoints of a product routing.

• Raw Material Inventory (RMI): material stocked at beginning of routing.

• Crib and Finished Goods Inventory (FGI): crib inventory is material held in a stockpoint at the end of a routing; FGI is material held in inventory prior to shipping to the customer.

• Cycle Time (CT): time between release of the job at the beginning of the routing until it reaches an inventory point at the end of the routing.

Factory Physics®

• Definition: A manufacturing system is a goal-oriented network of processes through which parts flow.

• Structure: Plant is made up of routings (lines), which in turn are made up of processes.

• Focus: Factory Physics® is concerned with the network and flows at the routing (line) level.

Parameters

• Descriptors of a Line:

• 1) Bottleneck Rate (rb): Rate (parts/unit time or jobs/unit time) of the process center having the highest long-term utilization.

• 2) Raw Process Time (T0): Sum of the long-term average process times of each station in the line.

• 3) Congestion Coefficient (): A unitless measure of congestion.• Zero variability case, = 0.• “Practical worst case,” = 1.• “Worst possible case,” = W0.

Note: we won’t use quantitatively,but point it out to recognize that lineswith same rb and T0 can behave verydifferently.

Parameters (cont.)

• Relationship:

Critical WIP (W0): WIP level in which a line having no congestion would achieve maximum throughput (i.e., rb) with minimum cycle time (i.e., T0).

• • W0 = rb T0

The Penny Fab• Characteristics:

• Four identical tools in series.• Each takes 2 hours per piece (penny).• No variability.• CONWIP job releases.

• Parameters:

rb =

T0 =

W0 =

=

0.5 pennies/hour

8 hours

0.5 8 = 4 pennies

0 (no variability, best case conditions)

The Penny FabThe Penny Fab

The Penny Fab (WIP=1)The Penny Fab (WIP=1)

Time = 0 hours


Time = 2 hours


Time = 4 hours


Time = 6 hours


Time = 8 hours


Time = 10 hours


Time = 12 hours


Time = 14 hours


Time = 16 hours

Penny Fab Performance

WIP TH CT THCT 1 0.125 8 1 2 3 4 5 6


Time = 0 hours


Time = 2 hours


Time = 4 hours


Time = 6 hours


Time = 8 hours


Time = 10 hours


Time = 12 hours


Time = 14 hours


Time = 16 hours


Time = 18 hours


WIP TH CT THCT 1 0.125 8 1 2 0.250 8 2 3 4 5 6


Time = 0 hours


Time = 2 hours


Time = 4 hours


Time = 6 hours


Time = 8 hours


Time = 10 hours


Time = 12 hours


Time = 14 hours


WIP TH CT THCT 1 0.125 8 1 2 0.250 8 2 3 0.375 8 3 4 0.500 8 4 5 6


Time = 0 hours


Time = 2 hours


Time = 4 hours


Time = 6 hours


Time = 8 hours


Time = 10 hours


Time = 12 hours


WIP TH CT THCT 1 0.125 8 1 2 0.250 8 2 3 0.375 8 3 4 0.500 8 4 5 0.500 10 5 6 0.500 12 6

TH vs. WIP: Best Case

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

TH

rrbb

WW00

1/T1/T00

CT vs. WIP: Best Case

02468

101214161820222426

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

CT

TT00

WW00

1/r1/rbb

Best Case Performance

• Best Case Law: The minimum cycle time (CTbest) for a given WIP level, w, is given by

The maximum throughput (THbest) for a given WIP level, w is given by,

otherwise.

if

,/

,CT 00

best

Ww

rw

T

b

otherwise.

if

,

,/TH 00

best

Ww

r

Tw

b

Best Case Performance (cont.)• Example: For Penny Fab, rb = 0.5 and T0 = 8, so W0 = 0.5 8 =

4,

which are exactly the curves we plotted.

otherwise.

4 if

,2

,8CTbest

w

w

otherwise.

4 if

,5.0

,8/THbest

ww

A Manufacturing Law

• Little's Law: The fundamental relation between WIP, CT, and TH over the long-term is:

• Insights:• Fundamental relationship• Simple units transformation• Definition of cycle time (CT = WIP/TH)

CTTHWIP

hrhr

partsparts

Penny Fab Two

10 hr

2 hr

5 hr 3 hr

Penny Fab Two

StationNumber

Number ofMachines

ProcessTime

StationRate

1 1 2 hr j/hr

2 2 5 hr j/hr

3 6 10 hr j/hr

4 2 3 hr j/hr

rb = ____________ T0 = ____________ W0 = ____________

0.5

0.4

0.6

0.67

0.4 p/hr 20 hr 8 pennies

Penny Fab Two Simulation (Time=0)

10 hr

2 hr

5 hr 3 hr

2


10 hr

2 hr

5 hr 3 hr

4

7


10 hr

2 hr

5 hr 3 hr

6

7

9


10 hr

2 hr

5 hr 3 hr

8

7

9


10 hr

2 hr

5 hr 3 hr

8

12

9

17


10 hr

2 hr

5 hr 3 hr

10

12

9

17


10 hr

2 hr

5 hr 3 hr

10

12

14

17

19


10 hr

2 hr

5 hr 3 hr

12

12

14

17

19


10 hr

2 hr

5 hr 3 hr

14

17

14

17

19

22


10 hr

2 hr

5 hr 3 hr

16

17

19

17

19

22

24


10 hr

2 hr

5 hr 3 hr

17

19

17

19

22

24


10 hr

2 hr

5 hr 3 hr

22

19

27

19

22

24

20


10 hr

2 hr

5 hr 3 hr

22

24

27

29

22

24

20

22


10 hr

2 hr

5 hr 3 hr

22

24

27

29

22

24 22

22

Note: job will arrive atbottleneck just in timeto prevent starvation.


10 hr

2 hr

5 hr 3 hr

27

24

27

29

32

24

2524

Note: job will arrive atbottleneck just in timeto prevent starvation.


10 hr

2 hr

5 hr 3 hr

27

29

27

29

32

34

25

27

And so on….Bottleneck will just stay busy; all others will starve periodically

Worst Case • Observation: The Best Case yields the minimum cycle time and

maximum throughput for each WIP level.

• Question: What conditions would cause the maximum cycle time and minimum throughput?

• Experiment:• set average process times same as Best Case (so rb and T0

unchanged)• follow a marked job through system• imagine marked job experiences maximum queueing

Worst Case Penny FabWorst Case Penny Fab

Time = 0 hours


Time = 8 hours


Time = 16 hours


Time = 24 hours


Time = 32 hours Note:

CT = 32 hours= 4 8 = wT0

TH = 4/32 = 1/8 = 1/T0

TH vs. WIP: Worst Case

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

TH

rrbb

WW00

1/T1/T00

Best CaseBest Case

Worst CaseWorst Case

CT vs. WIP: Worst Case

048

121620242832

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

CT

TT00

WW00

Best CaseBest Case


Worst Case Performance• Worst Case Law: The worst case cycle time for a given WIP

level, w, is given by,

• CTworst = w T0

The worst case throughput for a given WIP level, w, is given by,

• THworst = 1 / T0

• Randomness?

None - perfectly predictable, but bad!

Practical Worst Case • Observation: There is a BIG GAP between the Best Case and

Worst Case performance.

• Question: Can we find an intermediate case that:• divides “good” and “bad” lines, and• is computable?

• Experiment: consider a line with a given rb and T0 and:• single machine stations• balanced lines• variability such that all WIP configurations (states) are equally

likely

PWC Example – 3 jobs, 4 3 jobs, 4 stationsstations

State Vector State Vector1 (3,0,0,0) 11 (1,0,2,0) 2 (0,3,0,0) 12 (0,1,2,0) 3 (0,0,3,0) 13 (0,0,2,1) 4 (0,0,0,3) 14 (1,0,0,2) 5 (2,1,0,0) 15 (0,1,0,2) 6 (2,0,1,0) 16 (0,0,1,2) 7 (2,0,0,1) 17 (1,1,1,0) 8 (1,2,0,0) 18 (1,1,0,1) 9 (0,2,1,0) 19 (1,0,1,1) 10 (0,2,0,1) 20 (0,1,1,1)

clumped up states

spread out states

Practical Worst Case• Let w = jobs in system, N = no. stations in line, and t = process

time at all stations:

• CT(single) = (1 + (w-1)/N) t

• CT(line) = N [1 + (w-1)/N] t • = Nt + (w-1)t• = T0 + (w-1)/rb

• TH = WIP/CT • = [w/(w+W0-1)]rb

From Little’s LawFrom Little’s Law

Practical Worst Case Performance• Practical Worst Case Definition: The practical worst case

(PWC) cycle time for a given WIP level, w, is given by,

The PWC throughput for a given WIP level, w, is given by,

where W0 is the critical WIP.

br

wT

1CT 0PWC

,1

TH0

PWC brwW

w

TH vs. WIP: Practical Worst Case

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

TH

rrbb

WW00

1/T1/T00

Best CaseBest Case


PWCPWCGood (lean)Good (lean)

Bad (fat)Bad (fat)

CT vs. WIP: Practical Worst Case

048

121620242832

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

CT

TT00

WW00

Best CaseBest Case

Worst CaseWorst Case PWCPWC

Bad (fat)Bad (fat)

GoodGood(lean)(lean)

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16 18 20 22 24 26

WIP

TH

Penny Fab Two Performance

Worst Case

Penny Fab 2

Best Case

Practical Worst Case

1/T0

rb

W0

Note: processtimes in PF2have var equalto PWC.

But… unlike PWC, it hasunbalancedline and multimachine stations.

Penny Fab Two Performance (cont.)

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16 18 20 22 24 26

WIP

CT

Worst Case

Penny Fab 2

Best Case

Practical Worst C

ase

T0

1/rb

W0

Back to the HAL Case - Capacity Data

Process Rate (p/hr) Time (hr) Lamination 191.5 4.7 Machining 186.2 0.5 Internal Circuitize 114.0 3.6 Optical Test/Repair - Int 150.5 1.0 Lamination – Composites 158.7 2.0 External Circuitize 159.9 4.3 Optical Test/Repair - Ext 150.5 1.0 Drilling 185.9 10.2 Copper Plate 136.4 1.0 Procoat 117.3 4.1 Sizing 126.5 1.1 EOL Test 169.5 0.5 rb, T0 114.0 33.9

HAL Case - Situation

• Critical WIP: rbT0 = 114 33.9 = 3,869

• Actual Values:• CT = 34 days = 663 hours (at 19.5 hr/day)• WIP = 47,600 panels• TH = 71.8 panels/hour

• Conclusions:• Throughput is 63% of capacity• WIP is 12.3 times critical WIP• CT is 24.1 times raw process time

HAL Case - Analysis

• WIP Required for PWC to Achieve TH = 0.63rb?

•

586,6)1869,3(37.0

36.0)1(

37.0

63.0

63.01

0

0

Ww

rrWw

wTH bb

Much lower thanactual WIP!

Conclusion: actual system is much worse than PWC!

4.1051141869,3600,47

600,47

10

brWw

wTH Much higher

than actual TH!

TH Resulting from PWC with WIP = 47,600?

HAL Internal Benchmarking Outcome

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0 10,000 20,000 30,000 40,000 50,000

WIP

Th

rou

gh

pu

t (p

an

els/

hou

r)

Best

Worst

PWC

CurrentTH = 71.8WIP = 47,600“Lean" Region

“Fat" Region

Labor Constrained Systems• Motivation: performance of some systems are limited by labor

or a combination of labor and equipment.

• Full Flexibility with Workers Tied to Jobs:• WIP limited by number of workers (n)• capacity of line is n/T0

• Best case achieves capacity and has workers in “zones”• ample capacity case also achieves full capacity with “pick and

run” policy

Labor Constrained Systems (cont.)• Full Flexibility with Workers Not Tied to Jobs:

• TH depends on WIP levels• THCW(n) TH(w) THCW(w)• need policy to direct workers to jobs (focus on downstream is

effective)

• Agile Workforce Systems• bucket brigades• kanban with shared tasks• worksharing with overlapping zones• many others

Factory Dynamics Takeaways• Performance Measures:

• throughput• WIP• cycle time• service

• Range of Cases:• best case• practical worst case• worst case

• Diagnostics:• simple assessment based on rb, T0, actual WIP,actual TH• evaluate relative to practical worst case

Penny Fab Model

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